well, certainly my alerter service on my windows xp machine here is running logged on a local system. what account is yours using?
To quote XP itself, the Alerter "Notifies selected users and computers of administrative alerts. If the service is stopped, programs that use administrative alerts will not receive them. If this service is disabled, any services that explicitly depend on it will fail to start."
On my system its set as manual startup and turned off. This seems to be the default. On your system it may be set to automatic so you could try setting it to manual and then trying again, making sure that the service is stopped.
certainly I modify the page file with the alerter service turned off, so my guess is that something has changed yours to automatic, so try changing it to manual and ensuring its off. maybe reboot for good measure.
the alerter service would seem to have some dependencies (i.e services that need to be running in order for it to run) but there would seem to be no services that depend on it, so I can't see any reason why the alerter could not be turned off. so set to manual, not automatic.
If it is already manual, post back.